How to make nice race game camera?
This can be achieved by using the Slow Parent option.
Set an appropriate offset, and the parented object (in this case it is your camera) will always have that much delay to reach its target position. This provides for smoother parents and a side view when turning more reliably than using the Camera actuator. When using the Camera actuator, It does not behave as expected when the object it is following moves in the direction of the camera (for example, when the character is backing up)
using this method, you can have one camera for driving forward, and one camera for backing up, and both will reliably look where they are meant to.